Recovering Source Term and Temperature Distribution for Nonlocal Heat Equation
作者：
Highlights：
• The mth level fractional derivative, which is the generalization of well-known fractional derivatives such as Riemann-Liouville, Caputo and Hilfer, is considered.
• Two inverse problems of determining space dependent and time dependent source terms for Fractional heat equation with nonlocal boundary conditions and appropriate over-specified conditions are investigated.
• Ill-posedness of the considered inverse problems is proved in the sense of Hadamard.
• Eigenfunctions expansion method is used to construct the series solutions of both inverse problems. The existence and uniqueness results for the series solutions of the inverse problems are proved under some regularity conditions on the given data.
摘要
•The mth level fractional derivative, which is the generalization of well-known fractional derivatives such as Riemann-Liouville, Caputo and Hilfer, is considered.•Two inverse problems of determining space dependent and time dependent source terms for Fractional heat equation with nonlocal boundary conditions and appropriate over-specified conditions are investigated.•Ill-posedness of the considered inverse problems is proved in the sense of Hadamard.•Eigenfunctions expansion method is used to construct the series solutions of both inverse problems. The existence and uniqueness results for the series solutions of the inverse problems are proved under some regularity conditions on the given data.
论文关键词：Inverse problem,Generalized fractional derivative,Riesz basis,Mittag-Leffler functions
论文评审过程：Received 20 April 2022, Revised 25 September 2022, Accepted 29 September 2022, Available online 20 October 2022, Version of Record 20 October 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127610
